AFOQT Math Practice Test

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The volume of a cube is 64 cubic feet. What is the cube's surface area?

Correct! Wrong!

Explanation:
A cube is made up of equal length sides (s).
The volume of a cube is s x s x s.
Therefore, s=4 in this case (4x4x4=64).
A cube is made up of 6 squares, each with an area of s x s.
Therefore, the surface area of a cube is 6 x s x s = 6 x 4 x 4 = 96

What does A equal if F = M x A?

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Explanation:
If you divide both sides of the formula by M, then A = F/M

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Explanation:
3451/7562=.4563

The result of dividing 40 by.08 is

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Explanation:
40 divided by .08 = 500

With four shirts and five ties, how many different combinations of shirts and ties are possible?

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Explanation:
With each of the 4 shirts you can wear one of the 5 ties,
so the total number of combinations is 4 x 5 = 20

How much does ¾ pound of rice cost if a pound of rice costs \$4.20?

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Explanation:
\$4.20/4 = \$1.05
\$4.20 - \$1.05 = \$3.15

If 0.05z equals 1, then z equals

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Explanation:
Divide both sides by 0.05.
Therefore, z= 1/0.05=20

What does 4(x-y) + 7 equal if x = y?

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Explanation:
If x = y,
then you can subsitute x for y in the 2nd equation - so 4(x-x)+7 =
4(0)+7=7

The length of a shipping container is 327 feet, and the width is 15.3 feet. What is the volume of the container (rounded to the next whole number) if the height is 12.6 feet?

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Explanation:
V=LxWxH
L (327) x W(15.3) x H(12.6) =
63,039 cubic feet

What is the value of 4 cubed?

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Explanation:
4 cubed is 4 x 4 x 4 = 64

Which of the numbers below is NOT a prime number?

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Explanation:
93 is not a prime number since it is equal to 31 x 3.
If you add up the digits of a number and they are divisible by 3,
then the number is also divisible by 3.

Canmore has a temperature of -1°C. What is the temperature in degrees Fahrenheit using the formula F° = C°x (9/5) + 32?

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Explanation:
-1 × 1.8 + 32 = 30.2

What percentage of the office workforce is present if 1/3 of the staff is on vacation and 1/4 of those who are not on vacation are sick?

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Explanation:
If 1/3 are on vacation, then 2/3 are not. Of those 2/3 not on vacation,
3/4 are NOT sick. Therefore 2/3 x 3/4 are in the office (not on vacation and not sick)
= (2x3)/(3x4)=6/12=1/2

If x + y + 15 equals 30, and x + y equals z, then 40 - z equals

Correct! Wrong!

Explanation:
If x + y + 15 = 30, then z+ 15 = 30 (substitute x + y = z)
which means that z = 15. If z = 15, then 40 - z = 40 - 15 = 25

Correct! Wrong!

Explanation:
(10×3) = 30
12+18 = 30

A woman has a budget of Z dollars. How much money does she have left after she spends \$500?

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Explanation:
You need to subtract the money that she spent (\$500) from the original money that she had (Z).

Three baseball cards, three football cards, and six hockey cards make up a stack of sports cards. What is the chance that one of the cards chosen at random is a hockey card?

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Explanation:
There are 12 cards in total. Therefore,
the probability of picking a hockey card is 6/12 or 1/2.

What is the median of the data set including -3x, -6x, x, -9x, and 5x if x > 0?

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Explanation:
-9x, -6x, -3x, x, 5x
Since we know x is positive, the terms can be placed in order from smallest to largest.
By definition the median is the middle term in this list

There are 4 Chocolate Rolls, 3 Lollipops, 5 Toblerone, and 6 Starbursts in a bag of candy. What's the chance you'll get a lollipop if you pick one piece of candy at random?

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Explanation:
There are 18 total pieces of candy and 3 lollipops.
Therefore, the probability of picking one lollipop is 3/18 which simplifies to 1/6

The card set for a game consists of seven red cards and twenty-one green cards. What is the chance that one of these cards will be red if a player chooses one at random?

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Explanation:
There are a total of 28 cards – 7 red; 21 green. Therefore the probability of selecting an red card is: 7/28 = 1/4)

When 6a – 1 Equals 2(a + 1), what is the value of a?

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Explanation:
After distributing the 2, the equation is equivalent to 6a -1 = 2a + 2.
Simplifying, 4a = 3, so a = 3/4

When 5x – 5 Equals 6x + 8, what is the value of x?

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Explanation:
The goal here is to isolate the variable to one side with the constants on the other.
By subtracting 5x from both sides, you can rewrite the equation as: -5 = x + 8.
This simplifies to x = -13 when 8 is subtracted from both sides

What is the size of a rectangle with a diagonal of 25 meters and a width of 15 meters in square meters?

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Explanation:
The diagonal forms a right triangle with the width and the length acting as legs.
Using the Pythagorean theorem, the length of the triangle will be √25^2 – 15^2 =
√400 = 20, and the area will be 20 x 15 = 300

Each member in a room is a sophomore or freshman. The number of freshmen in the room outnumbers the number of sophomores by a factor of seven. The number of individuals in the room could be one of the following. Make a list of all such numbers.

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Explanation:
If the number of sophomores in the room is x, then the number of freshman is 7x.
The total number of people in the room is 7x + x = 8x. The number of people in the
room (8x) must be a multiple of 8.)

At vertex X, the exterior angle of the triangle XYZ is 130°, whereas at vertex Y, the exterior angle is 110°. At vertex Z, what is the internal angle?

Correct! Wrong!

Explanation:
The sum of the exterior angles of any polygon is 360°, so the exterior angle at vertex Z is 360°-130°-110° = 120°.
However, this is not the value of the question asked. Since the sum of the interior angle of a polygon and its
exterior angle is 180°, the interior angle at vertex Z is 180°-120° = 60°